Is there a way to check whether an integer is a prime or not in O(log(n))?

Hi Codeforces community!

I was doing a problem like this: Given a string s, reverse a substring of it in each query, and print the final string after all queries. Constraints are 1 ≤ |S|, Q ≤ 10^5. I have seen many solutions using tree algorithms, is it possible to solve this problem without using tree algorithms?

Thanks!